The nation’s top immigration and border officials are urging Homeland Security Secretary Kirstjen Nielsen to detain and prosecute all parents caught crossing the Mexican border illegally with their children, a stark change in policy that would result in the separation of families that until now have mostly been kept together.

If approved, the zero-tolerance measure could split up thousands of families, although officials say they would not prosecute those who turn themselves in at legal ports of entry and claim asylum. More than 20,000 of the 30,000 migrants who sought asylum during the first quarter — the period from October-December — of the current fiscal year crossed the border illegally.

In a memorandum that outlines the proposal and was obtained by The Washington Post, officials say that threatening adults with criminal charges and prison time would be the “most effective” way to reverse the steadily rising number of attempted crossings. Most parents now caught crossing the border illegally with their children are quickly released to await civil deportation hearings.

The memo sent to Nielsen on Monday — and signed by acting Director of Immigration and Customs Enforcement Thomas Homan, Director of Citizenship and Immigration Services L. Francis Cissna and Customs and Border Protection Commissioner Kevin K. McAleenan — said attempted crossings by parents with children increased to nearly 700 a day last week, the highest level since 2016. The officials predicted that the number will continue to rise if Nielsen does not act.

Lee Gelernt, an attorney with the American Civil Liberties Union who has filed a federal lawsuit in California over earlier instances of family separations at the border, said the proposal would make “children as young as 2 and 3 years old pawns in a cruel public policy experiment.”

President Trump has repeatedly vowed to crack down on illegal border crossings. He renewed that pledge this month, signing his second directive ordering the end of “catch and release,” a term used by critics to describe the current practice.

The Post subsequently reported that the government has released about 100,000 parents and children since Trump took office. Officials say they are forced to do so by federal laws and court rulings that limit the detention of children, in addition to limits imposed by a lack of detention space for adults.

After Trump’s directive, issued April 6, Attorney General Jeff Sessions ordered U.S. attorneys along the border from Texas to California to prosecute “to the extent practicable” all illegal border crossers referred to them by the Department of Homeland Security. Monday’s memo urged Nielsen to refer for prosecution “100 percent” of the adults held at the border, “including those initially arriving or apprehended with minors.”

Such a policy would mean separating parents and children, because the parents would be placed in criminal detention, where children cannot be held.

The memo said the Trump administration tried this approach in the Border Patrol’s El Paso sector, which covers West Texas and New Mexico, between July 2017 and November 2017.

Afterward, the number of families trying to cross illegally plunged by 64 percent, the memo said. “This decrease was attributed to the prosecution of adults . . . for illegal entry,” the memo said. “ Of note, the numbers began rising again after the initiative was paused.”

In a statement, Homeland Security spokeswoman Katie Waldman said the agency “is looking at all options in conjunction with the Attorney General’s zero tolerance policy for those illegally crossing the border. We will not comment further on internal deliberations. Again, DHS does not have a policy of separating families at the border for deterrence purposes. DHS does, however, have a legal obligation to protect the best interests of the child whether that be from human smugglings, drug traffickers, or nefarious actors who knowingly break our immigration laws and put minor children at risk.”

Most immigrants caught crossing the border illegally have typically faced civil deportation hearings to determine whether they may stay in the United States. But border-crossers can be charged criminally as well.

Over the past two decades, in an attempt to deter illegal crossings, criminal prosecutions have increased sharply — from fewer than 10,000 in 1996 to a high of 90,000 in 2013,according to TRAC, a Syracuse University organization that monitors immigration prosecutions.

The most common criminal charge is “improper entry by alien” — or illegal entry — the charge recommended in the memo. For first offenders, it is typically a federal misdemeanor punishable by up to six months in prison or fines. Repeat offenders can be fined or imprisoned for up to two years or charged with the more serious offense of “illegal reentry.”

The memo says that referring for prosecution all immigrants caught sneaking across the border “would likely have the most effective impact,” though it may also present an increased risk of legal challenges.

The officials present Nielsen with two other options: prosecuting all single adults, and ramping up government resources accordingly; or working with prosecutors to charge as many adults as possible, using existing resources, which the memo said would be the least effective approach.

Philip G. Schrag, a Georgetown law professor and asylum expert, said that expanding the forced separation of parents and children could cause severe psychological harm to families that ultimately might have legal grounds under federal asylum law to remain in the United States permanently.

“I think it’s absolutely wrenching psychologically and terrible for both the children and the parents,” he said. “What are we doing to those children psychologically that will haunt us years down the road if they become Americans?”

Federal officials say asylum applications have skyrocketed in recent years, raising concerns about fraud. Advocates for immigrants say those seeking asylum have legitimate claims under federal law and are fleeing some of the world’s most dangerous countries.

After Trump took office, attempted border crossings plunged to their lowest levels in 46 years. But apprehensions have risen 203 percent in the past year, and they jumped 37 percent from February to March, the largest month-to-month increase since 2011.

For the most part, federal officials historically have separated parents and children only when they were unsure whether they were related to one another. But The Post reported last year that stricter measures were being floated, and The Post last month told the story of a Salvadoran woman who was separated from her three children after crossing the border in December. They were reunited in March. The New York Times reported last week that according to data from the U.S. Office of Refugee Resettlement, hundreds of children have been taken from their parents at the border since October.

Nielsen told a congressional committee this month that her agency does not separate families to punish parents and that the current standard is to keep families together “as long as operationally possible.”

When the government separates families, she said, it does so to “protect the children” and to verify that they are related to the adults, and to establish that the children are not being trafficked.

McAleenan also testified this month that family separation is “very rare,” occurring in about 1.4 percent of all cases of detained families.

At a hearing Thursday, Sen. Kamala D. Harris (D-Calif.) said DHS officials have made “inconsistent statements” about the separation of families. James W. McCament, deputy undersecretary of the Office of Strategy, Policy, and Plans at DHS, responded: “We do not currently have a policy of separating women and children.”